Claims:We Claim:
1. A processor implemented method (200), comprising:
obtaining, via one or more hardware processors, time series data specific to a plurality of sensors associated with a device (202);
computing, via the one or more hardware processors, a first order derivative of (i) one or more timestamps and (ii) coordinates of positional data from the obtained time series data (204);
converting, via the one or more hardware processors, the first order derivative of the coordinates of positional data to a set of absolute positional data (206);
computing, via the one or more hardware processors, a velocity for a current timestamp based on the first order derivative of the one or more timestamps and the absolute positional data (208);
computing, via the one or more hardware processors, an acceleration for the current timestamp based on a pre-computed second order derivative of the one or more timestamps and the absolute positional data (210);
iteratively computing, via the one or more hardware processors, an absolute positional data corresponding to each missing positional value of one or more positional sensors from the plurality of sensors at a next timestamp based on the velocity and the acceleration of the current timestamp, until a last missing positional value is populated (212);
mapping, via the one or more hardware processors, the computed absolute positional data corresponding to each missing positional value of one or more positional sensors with a corresponding positional data from the set of absolute positional data to obtain mapped positional data (214); and
iteratively performing, the steps of:
constructing, via the one or more hardware processors, a data-driven dependency graph using the mapped positional data as a root node of a current iteration (216a); and
populating, via the one or more hardware processors, one or more missing values corresponding to positional data associated with a set of sensors, wherein the one or more missing values serves as a set of child nodes associated with the root node of the current iteration, and wherein the set of child nodes serves as a root node for a subsequent iteration (216b),
until a last child node is populated with a missing value, wherein the last child node belongs to a plurality of child nodes in the data-driven dependency graph.

2. The processor implemented method of claim 1, wherein the velocity for the specific timestamp is computed based on a ratio of the first order derivative of the one or more timestamps and the absolute positional data.

3. The processor implemented method of claim 1, wherein the step of populating the one or more missing values corresponding to the positional data associated with the set of sensors is based on a machine learning based prediction technique.

4. A system (100), comprising:
a memory (102) storing instructions;
one or more communication interfaces (106); and
one or more hardware processors (104) coupled to the memory (102) via the one or more communication interfaces (106), wherein the one or more hardware processors (104) are configured by the instructions to:
obtain time series data specific to a plurality of sensors associated with a device;
compute a first order derivative of (i) one or more timestamps and (ii) coordinates of positional data from the obtained time series data;
convert the first order derivative of the coordinates of positional data to a set of absolute positional data;
compute a velocity for a current timestamp based on the first order derivative of the one or more timestamps and the absolute positional data;
compute an acceleration for the current timestamp based on a pre-computed second order derivative of the one or more timestamps and the absolute positional data;
iteratively compute an absolute positional data corresponding to each missing positional value of one or more positional sensors from the plurality of sensors at a next timestamp based on the velocity and the acceleration of the current timestamp, until a last missing positional value is populated;
map the computed absolute positional data corresponding to each missing positional value of one or more positional sensors with a corresponding positional data from the set of absolute positional data to obtain mapped positional data; and
iteratively perform:
construct a data-driven dependency graph using the mapped positional data as a root node of a current iteration; and
populate one or more missing values corresponding to positional data associated with a set of sensors, wherein the one or more missing values serves as a set of child nodes associated with the root node of the current iteration, and wherein the set of child nodes serves as a root node for a subsequent iteration,
until a last child node is populated with a missing value, wherein the last child node belongs to a plurality of child nodes in the data-driven dependency graph.

5. The system of claim 4, wherein the velocity for the specific timestamp is computed based on a ratio of the first order derivative of the one or more timestamps and the absolute positional data.

6. The system of claim 4, wherein the one or more missing values corresponding to the positional data associated with the set of sensors are populated based on a machine learning based prediction technique.

Dated this 28th day of December 2021

Tata Consultancy Services Limited
By their Agent & Attorney

(Adheesh Nargolkar)
of Khaitan & Co
Reg No IN-PA-1086 , Description:FORM 2

THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003

COMPLETE SPECIFICATION
(See Section 10 and Rule 13)

Title of invention:
MULTI PASS MISSING SENSOR VALUE IMPUTATION TO A TIME SERIES DATA COMPRISING POSITIONAL DATA

Applicant
Tata Consultancy Services Limited
A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th floor,
Nariman point, Mumbai 400021,
Maharashtra, India

Preamble to the description:
The following specification particularly describes the invention and the manner in which it is to be performed.
TECHNICAL FIELD
[001] The disclosure herein generally relates to sensor data analytics, and, more particularly, to multi pass missing sensor value imputation to a time series data comprising positional data.

BACKGROUND
[002] In manufacturing and aviation industry, a very common problem is to handle the dataset with missing data. Any machine part is normally connected with a plethora of sensors including location sensors. In many use cases there is a requirement to track and analyse operating conditions of a machine (or machine part) moving over time such as engine of a vehicle or flights. One of such location sensors used to localize in outdoor scenario is a Global Positioning System (GPS) sensor. This plays an important role in such analytics as it can be used to (i) monitor the operating conditions of a machine when the location information is very much required such as the engine of a vehicle is dependent on the location (traffic congestion inside a city or inclining slope in a hilly area), and (ii) track the route of the vehicle and recommend an optimal path. However, latitude and longitude data captured by the GPS sensor is often noisy and includes lots of missing data. For instance, such scenarios include (a) when the GPS is blocked by certain areas because of administrative constraints, (b) it is often unreliable because the device used to sense the GPS is not very accurate, (c) it may also become noisy due to the employed communication channel. Thus, it is imperative, as a pre-processing step, to populate missing latitudes and longitudes for better analytics.

SUMMARY
[003] Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one aspect, there is provided a processor implemented method for multi pass missing sensor value imputation to a time series data comprising positional data. The method comprises obtaining, via one or more hardware processors, time series data specific to a plurality of sensors associated with a device; computing, via the one or more hardware processors, a first order derivative of (i) one or more timestamps and (ii) coordinates of positional data from the obtained time series data; converting, via the one or more hardware processors, the first order derivative of the coordinates of positional data to a set of absolute positional data; computing, via the one or more hardware processors, a velocity for a current timestamp based on the first order derivative of the one or more timestamps and the absolute positional data; computing, via the one or more hardware processors, an acceleration for the current timestamp based on a pre-computed second order derivative of the one or more timestamps and the absolute positional data; iteratively computing, via the one or more hardware processors, an absolute positional data corresponding to each missing positional value of one or more positional sensors from the plurality of sensors at a next timestamp based on the velocity and the acceleration of the current timestamp, until a last missing positional value is populated; mapping, via the one or more hardware processors, the computed absolute positional data corresponding to each missing positional value of one or more positional sensors with a corresponding positional data from the set of absolute positional data to obtain mapped positional data; and iteratively performing, the steps of: constructing, via the one or more hardware processors, a data-driven dependency graph using the mapped positional data as a root node of a current iteration; and populating, via the one or more hardware processors, one or more missing values corresponding to positional data associated with a set of sensors, wherein the one or more missing values serves as a set of child nodes associated with the root node of the current iteration, and wherein the set of child nodes serves as a root node for a subsequent iteration, until a last child node is populated with a missing value, wherein the last child node belongs to a plurality of child nodes in the data-driven dependency graph.
[004] In an embodiment, the velocity for the specific timestamp is computed based on a ratio of the first order derivative of the one or more timestamps and the absolute positional data.
[005] In an embodiment, the step of populating the one or more missing values corresponding to positional data associated with the set of sensors is based on a machine learning based prediction technique.
[006] In another aspect, there is provided a processor implemented system for multi pass missing sensor value imputation to a time series data comprising positional data. The system comprises: a memory storing instructions; one or more communication interfaces; and one or more hardware processors coupled to the memory via the one or more communication interfaces, wherein the one or more hardware processors are configured by the instructions to: obtain time series data specific to a plurality of sensors associated with a device; compute a first order derivative of (i) one or more timestamps and (ii) coordinates of positional data from the obtained time series data; convert the first order derivative of the coordinates of positional data to a set of absolute positional data; compute a velocity for a current timestamp based on the first order derivative of the one or more timestamps and the absolute positional data; compute an acceleration for the current timestamp based on a pre-computed second order derivative of the one or more timestamps and the absolute positional data; iteratively compute an absolute positional data corresponding to each missing positional value of one or more positional sensors from the plurality of sensors at a next timestamp based on the velocity and the acceleration of the current timestamp, until a last missing positional value is populated; map the computed absolute positional data corresponding to each missing positional value of one or more positional sensors with a corresponding positional data from the set of absolute positional data to obtain mapped positional data; and iteratively perform, the steps of: constructing a data-driven dependency graph using the mapped positional data as a root node of a current iteration; and populating one or more missing values corresponding to positional data associated with a set of sensors, wherein the one or more missing values serves as a set of child nodes associated with the root node of the current iteration, and wherein the set of child nodes serves as a root node for a subsequent iteration, until a last child node is populated with a missing value, wherein the last child node belongs to a plurality of child nodes in the data-driven dependency graph.
[007] In an embodiment, the velocity for the specific timestamp is computed based on a ratio of the first order derivative of the one or more timestamps and the absolute positional data.
[008] In an embodiment, the one or more missing values corresponding to positional data associated with the set of sensors are populated based on a machine learning based prediction technique.
[009] In yet another aspect, there are provided one or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause multi pass missing sensor value imputation to a time series data comprising positional data, comprising obtaining, via the one or more hardware processors, time series data specific to a plurality of sensors associated with a device; computing, via the one or more hardware processors, a first order derivative of (i) one or more timestamps and (ii) coordinates of positional data from the obtained time series data; converting, via the one or more hardware processors, the first order derivative of the coordinates of positional data to a set of absolute positional data; computing, via the one or more hardware processors, a velocity for a current timestamp based on the first order derivative of the one or more timestamps and the absolute positional data; computing, via the one or more hardware processors, an acceleration for the current timestamp based on a pre-computed second order derivative of the one or more timestamps and the absolute positional data; iteratively computing, via the one or more hardware processors, an absolute positional data corresponding to each missing positional value of one or more positional sensors from the plurality of sensors at a next timestamp based on the velocity and the acceleration of the current timestamp, until a last missing positional value is populated; mapping, via the one or more hardware processors, the computed absolute positional data corresponding to each missing positional value of one or more positional sensors with a corresponding positional data from the set of absolute positional data to obtain mapped positional data; and iteratively performing, the steps of: constructing, via the one or more hardware processors, a data-driven dependency graph using the mapped positional data as a root node of a current iteration; and populating, via the one or more hardware processors, one or more missing values corresponding to positional data associated with a set of sensors, wherein the one or more missing values serves as a set of child nodes associated with the root node of the current iteration, and wherein the set of child nodes serves as a root node for a subsequent iteration, until a last child node is populated with a missing value, wherein the last child node belongs to a plurality of child nodes in the data-driven dependency graph.
[010] In an embodiment, the velocity for the specific timestamp is computed based on a ratio of the first order derivative of the one or more timestamps and the absolute positional data.
[011] In an embodiment, the step of populating one or more missing values corresponding to positional data associated with the set of sensors is based on a machine learning based prediction technique.
[012] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS
[013] The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles:
[014] FIG. 1 depicts an exemplary system for multi pass missing sensor value imputation to a time series data comprising positional data, in accordance with an embodiment of the present disclosure.
[015] FIG. 2 depicts an exemplary flow chart illustrating a method for multi pass missing sensor value imputation to a time series data comprising positional data, using the system 100 of FIG. 1, in accordance with an embodiment of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS
[016] Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the scope of the disclosed embodiments.
[017] As mentioned earlier, tracking, and analysing operation conditions of a machine plays a critical role in sensor analytics when the location information is very much required such as the engine of a vehicle is dependent on the location (traffic congestion inside a city or inclining slope in a hilly area), and track the route of the vehicle and recommend an optimal path. However, the latitude and longitude data captured by the GPS sensor is often noisy and includes lots of missing data. For instance, such scenarios include (a) when the GPS is blocked by certain areas because of administrative constraints, (b) it is often unreliable because of the device used to sense the GPS is not very accurate, (c) it may also become noisy due to communication channel. There are a few existing approaches such as linear interpolation technique and the like to address the above problem. However, such techniques fail to capture or populate missing values in the sensor data and the captured data is not uniformly sampled and thus are inefficient and may be inaccurate.
[018] Embodiments of the present disclosure provide system and method for multi pass missing sensor value imputation to a time series data comprising positional data. More specifically, the system and method of the present disclosure address the above problem and overcome the shortcomings/disadvantages of the existing techniques by (i) considering unequal sampling of sensor data over time, (ii) performing an inverse mapping between distance and latitude-longitude data to populate missing values of sensors, (iii) populating the missing values of sensors based on an assumption of constant velocity within a small instance of time and even when there is an acceleration at any time instance.
[019] Referring now to the drawings, and more particularly to FIGS. 1 through 2, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method.
[020] FIG. 1 depicts an exemplary system 100 for multi pass missing sensor value imputation to a time series data comprising positional data, in accordance with an embodiment of the present disclosure. In an embodiment, the system 100 includes one or more hardware processors 104, communication interface device(s) or input/output (I/O) interface(s) 106 (also referred as interface(s)), and one or more data storage devices or memory 102 operatively coupled to the one or more hardware processors 104. The one or more processors 104 may be one or more software processing components and/or hardware processors. In an embodiment, the hardware processors can be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) is/are configured to fetch and execute computer-readable instructions stored in the memory. In an embodiment, the system 100 can be implemented in a variety of computing systems, such as laptop computers, notebooks, hand-held devices (e.g., smartphones, tablet phones, mobile communication devices, and the like), workstations, mainframe computers, servers, a network cloud, and the like.
[021] The I/O interface device(s) 106 can include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like and can facilitate multiple communications within a wide variety of networks N/W and protocol types, including wired networks, for example, LAN, cable, etc., and wireless networks, such as WLAN, cellular, or satellite. In an embodiment, the I/O interface device(s) can include one or more ports for connecting a number of devices to one another or to another server.
[022] The memory 102 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random-access memory (SRAM) and dynamic-random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment, a database 108 is comprised in the memory 102, wherein the database 108 comprises timeseries data corresponding to one or more machines and/or Internet of Things (IoT) devices. The database 108 further comprises information pertaining to first order derivative computation, absolute positional data, velocity, second order derivative computation for computing acceleration, mapped positional data, data driven dependency graphs (D3G) for using the mapped positional data for each root node, missing values being populated for each child node in the D3G, and the like. The memory 102 further includes one or more machine learning based prediction techniques such as (i) Support Vector Regression, (ii) Random Forest Regression, and (iii) Long Short-Term Memory (LSTM) based prediction technique, and the like. The above machine learning based prediction technique(s) which when executed by the one or more hardware processors 104 enable the system 100 to perform the method described herein. The memory 102 further comprises (or may further comprise) information pertaining to input(s)/output(s) of each step performed by the systems and methods of the present disclosure. In other words, input(s) fed at each step and output(s) generated at each step are comprised in the memory 102 and can be utilized in further processing and analysis.
[023] FIG. 2 depicts an exemplary flow chart illustrating a method 200 for multi pass missing sensor value imputation to a time series data comprising positional data, using the system 100 of FIG. 1, in accordance with an embodiment of the present disclosure. In an embodiment, the system(s) 100 comprises one or more data storage devices or the memory 102 operatively coupled to the one or more hardware processors 104 and is configured to store instructions for execution of steps of the method by the one or more processors 104. The steps of the method of the present disclosure will now be explained with reference to components of the system 100 of FIG. 1, and the flow diagram as depicted in FIG. 2.
[024] In an embodiment of the present disclosure, at step 202 the one or more hardware processors 102 obtain time series data specific to a plurality of sensors associated with a device (e.g., vehicle, IoT device, airplane, car, smart devices, etc.). In an embodiment, the time series data specific to the plurality of sensors may also be referred as ‘sensor observation’ (or ‘data’ or ‘sensor data’ and the like) and interchangeably used herein after. The data is sorted in the order of time stamp and each row in the input data represents a sensor observation at a particular instance of time. Assuming, the time stamps of the sensor observations are represented as t0, t1, …, tn, etc. Below Table 1 depicts an exemplary time series data specific to the plurality of sensors.
Table 1
Year Month Day Time latitude longitude
2017 10 14 18:33:56 37.29845 75.07804
2017 10 14 18:58:16 75.09457
2017 10 14 19:07:16 37.28774 75.10043
2017 10 14 19:17:49 37.28772 75.1006
2017 10 14 19:20:33 37.28773 75.10059
2017 10 14 20:08:12 37.28943 75.10169
2017 10 14 20:37:56 37.29064 75.10177
2017 10 14 20:44:18 37.30097 75.10204
2017 10 14 21:08:33 75.09815
2017 10 14 21:17:38 37.28938
2017 10 14 22:38:40 37.26622
2017 10 15 23:06:42 75.13142
2017 10 16 1:36:43 37.29813 75.10276
2017 10 16 1:55:55 75.07817
2017 10 16 3:54:45 37.19139 75.00694
2017 10 16 4:09:47 37.27996
2017 10 16 4:12:08 37.27746 75.09591
… … … … … …
2017 10 16 18:37:46 37.289766 75.101765

[025] In an embodiment of the present disclosure, at step 204 the one or more hardware processors 102 compute a first order derivative of (i) one or more timestamps and (ii) coordinates of positional data from the obtained time series data. The first order derivative is computed as dt = tn - tn-1. Below Table 2 depicts an exemplary first order derivative of (i) one or more timestamps and (ii) coordinates of positional data from the obtained time series data, in accordance with an embodiment of the present disclosure.
Table 2
Delta_t (dt) latitude longitude del_lat (d(lat)) del_long (d(long))
0:24:20 37.298448 75.078041 0.016524
0:09:00 75.094565 0.00586
0:10:33 37.287739 75.100425 1.6E-05 0.000178
0:02:44 37.287723 75.100603 4E-06 1.6E-05
0:47:39 37.287727 75.100587 0.001701 0.001107
0:29:44 37.289428 75.101694 0.001211 7.9E-05
0:06:22 37.290639 75.101773 0.010332 0.000267
0:24:15 37.300971 75.10204 0.003892
0:09:05 75.098148
1:21:02 37.289379 0.023156 0
0:28:02 37.266223
2:30:01 75.131421 0.028662
0:19:12 37.298131 75.102759 0.024593
1:58:50 75.078166 0.07123
0:15:02 37.191387 75.006936 0.088573
0:02:21 37.27996 0.002499
0:02:39 37.277461 75.095912 0.02004 0.000874
… … … … …
- 37.289766 75.101765 - -

[026] Similarly, the d(lat) and d(long) values for a current timestamp are also computed based on an absolute difference between corresponding latitude/longitude value of current timestamp and a latitude/longitude value of a subsequent timestamp. For instance, for 0:10:33 dt, the d(lat) is computed by taking an absolute difference of 37.287739 and 37.287723 (e.g., ABS(37.287723-37.287739) = 1.6E-05. Similarly, for instance, for 0:10:33 dt, the d(long) is computed by taking an absolute difference of 75.100425 and 75.100603 (e.g., ABS(75.100603-75.100425) = 0.000178. It is to be noted and understood that the last row has no values for dt, d(lat) and d(long), since there are no subsequent timestamp and latitude/longitude values for computing.
[027] In an embodiment of the present disclosure, at step 206 the one or more hardware processors 102 convert the first order derivative of the coordinates of positional data to a set of absolute positional data. In an embodiment of the present disclosure, the first order derivative of the coordinates of positional data is converted to obtain a set of absolute positional data by way of following non-construing expressions:
Function f and g are defined as
a) f(d(lat)) = d(lat)*68.9722
b) g(d(long), d(lat)) = d(lat)*68.9722* Cos(p*long/180)
Below Table 3 depicts an exemplary set of absolute positional data (e.g., abs_pos_x and abs_pos_y as depicted below) computed based on the above a) and b) expressions:
Table 3
Abs_pos_x Abs_pos_y
0 0
0 0
0.001103555 0.001103555
0.000275889 0.000275889
0.117321712 0.117321712
0.083525334 0.083525334
0.71262077 0.71262077
0 0
0 0
1.597120263 1.597120263
0 0
0 0
0 0
0 0
6.109074671 6.109074671
0.172361528 0.172361528
1.382202888 1.382202888
… …
0 0

[028] In an embodiment of the present disclosure, at step 208 the one or more hardware processors 102 compute a velocity for a current timestamp based on the first order derivative of the one or more timestamps and the absolute positional data. In an embodiment, the velocity for the specific timestamp is computed based on a ratio of the first order derivative of the one or more timestamps and the absolute positional data. Velocity computed above is obtained by first computing displacement between two samples/sensor observations captured at tn and tn-1 as shown in expression below:
s = SQRT((sx)2 + (sy)2)
Below Table 4 depicts an exemplary displacement between two samples/sensor observations (e.g., also referred as ‘Euclidean distance’/Eucl_dist and interchangeably used herein).
Table 4
Eucl_dist
0
0
0.001560663
0.000390166
0.165917957
0.11812266
1.007797958
0
0
2.258669137
0
0
0
0
8.639536253
0.24375601
1.95473007
…
0

[029] Then, velocity is computed. For instance, velocity for the specific timestamp is also referred as instant velocity at tn and computed based on below non-construing expression as:
vt = (ds)/ (dt)
[030] Below Table 5 depicts an exemplary velocity (e.g., also referred as ‘vel’ and interchangeably used herein) computed for the specific timestamp based on the first order derivative of the one or more timestamps and the absolute positional data.
Table 5
vel
0
0
0.213019368
0.205550701
5.014099841
5.720738711
227.9417372
0
0
40.13760046
0
0
0
0
827.5564659
149.365385
1062.192944
…

[031] In an embodiment of the present disclosure, at step 210 the one or more hardware processors 102 compute an acceleration for the current timestamp based on a second order derivative of the one or more timestamps (e.g., a pre-computed second order derivative of the one or more timestamps) and the absolute positional data. For instance, acceleration is computed using the below non-construing expression:
acceleration at tn as at = (dv)/ (dt) or accn=del(vel)/del(t) or accn=del^2(s)/del(t^2)
The second order derivative of the one or more timestamps (e.g., also referred as ‘2nd_der_t’ or the pre-computed second order derivative of the one or more timestamps and interchangeably used herein) is computed/obtained as depicted in Table 6.
Table 6
2nd_der_t
0:33:20
0:19:33
0:13:17
0:50:23
1:17:23
0:36:06
0:30:37
0:33:20
1:30:07
1:49:04
2:58:03
2:49:13
2:18:02
2:13:52
0:17:23
0:05:00
0:02:47
…
0:00:00

Table 7 depicts del(vel) (or (dv) being computed:
Table 7
del(vel) (or (dv)
0
0.213019368
-0.007468667
4.80854914
0.70663887
222.2209985
-227.9417372
0
40.13760046
-40.13760046
0
0
0
827.5564659
-678.1910809
912.8275588
-409.055591
…

The acceleration is computed based of the one or more timestamps and the absolute positional data. In an embodiment of the present disclosure, the second order derivative for a current timestamp (e.g., say t1) is obtained by taking a difference of t1 and t3 (e.g., 19:07:16-18:33:56). Below Table 8 depicts an exemplary acceleration computed for the current timestamp based on the second order derivative of the one or more timestamps and the absolute positional data:
Table 8
Accn= del(vel)/del(t)
0
15.69042915
-0.809652237
137.4325656
13.1496012
8864.217113
-10720.83075
0
641.3702015
-529.9340892
0
0
0
8902.001824
-56179.97065
262894.3369
-211631.1561
…

[032] In an embodiment of the present disclosure, at step 212 the one or more hardware processors 102 iteratively compute an absolute positional data corresponding to each missing positional value of one or more positional sensors from the plurality of sensors at a next timestamp based on the velocity and the acceleration of the current timestamp, until a last missing positional value is populated. When there is a missing value in latitude and longitude at time instance, say in tm, instance velocity and acceleration as computed above at time tm-1 are used to estimate the displacement s at time tm using the expression as given below:
sm = vm-1* dt + ½. am-1. (dt)* (dt)
Table 9 depicts an exemplary absolute positional data being computed for ‘n’ iterations. More specifically, present disclosure depicts the absolute positional data being computed for up to ‘4’ iterations (shall not be construed as limiting the scope of the present disclosure.
Table 9
It_1 It_2 It_3 It_4
0 0 0 0
0 0 0
0.001561 0.001561 0.001561 0.001561
0.00039 0.00039 0.00039 0.00039
0.165918 0.165918 0.165918 0.165918
0.118123 0.118123 0.118123 0.118123
1.007798 1.007798 1.007798 1.007798
-1.11258 -1.11258 -1.11258 -1.11258
0 -0.01874 -0.01874 -0.01874
2.258669 2.258669 2.258669 2.258669
-3.09773 -3.09773 -3.09773 -3.09773
0 -0.06031 -0.06031 -0.06031
0 0 -0.00628 -0.00628
0 0 0 -8.4E-05
8.639536 8.639536 8.639536 8.639536
0.243756 0.243756 0.243756 0.243756
1.95473 1.95473 1.95473 1.95473
… … … …

[033] Direction of the displacement is also assumed to be constant with the previous time instance and it is computed as shown in below expression:
?m = tan-1 [(sy/sx)m-1]
Below Table 10 depicts ?m:
Table 10
? (theta)
1.570796
1.570796
0.785398163
0.785398163
0.785398163
0.785398163
0.785398163
1.570796
1.570796
0.785398163
1.570796
1.570796
1.570796
1.570796
0.785398163
0.785398163
0.785398163
…
1.570796

[034] Now mapped positional data sx, and sy at time tm are computed as
smx = sm*cos(?m) and
smy = sm*sin(?m)
[035] Table 11 depicts new values for mapped positional data sx, and sy as shown below:
Table 11
new_s_x new_s_y


0.00110355520015425000 0.00110355520015371000
0.00027588879979352500 0.00027588879979352400
0.11732171220028800000 0.11732171219806900000
0.08352533419985190000 0.08352533419984390000
0.71262077039987800000 0.71262077039909400000
-1.11258261267746000000 -0.00000036358631980011
-0.01873620024821420000 -0.00000000612289462163
1.59712026320001000000 1.59712026320001000000
-3.09773158682764000000 -0.00000101232287342039
-0.06030537649356600000 -0.00000001970748927191
-0.00628250803030773000 -0.00000000205309156176
-0.00008376677373743630 -0.00000000002737455416
6.10907467059340000000 6.10907467059340000000
0.17236152780001700000 0.17236152780001700000
1.38220288800648000000 1.38220288799019000000
… …

[036] In an embodiment of the present disclosure, at step 214 the one or more hardware processors 102 map the computed absolute positional data corresponding to each missing positional value of one or more positional sensors with a corresponding positional data from the set of absolute positional data to obtain mapped positional data. For instance, the system 100 applies inverse transformation (f-1(d(lat))) to get the missing latitude (latm) from smx and g-1(d(long), d(lat)) to get the missing longitude (longm) from smy. Below Table 12 depicts mapped positional data obtained:
Table 12
del_lat_comp del_long_comp
0.016524
0.00586
1.6E-05 0.000177978
4E-06 1.58682E-05
0.001701 0.001106999
0.001211 7.89773E-05
0.010332 0.000266984
-0.016130885 282.74328
-0.000271649 282.74328
0.023156 0
-0.044912756 282.74328
-0.000874343 282.74328
-9.10875E-05 282.74328
-1.2145E-06 282.74328
0.088573 0
0.002499 0
0.02004 0.000873997
… …

[037] For instance, in the above Table 12, value of del_lat, 1.6E-05 is obtained by dividing 0.001103555 by 68.9722. Similarly, value of del_long, 0.000177978 is obtained by computing 180*Cos-1(0.00110355520015371/ 0.00110355520015425).
[038] In an embodiment of the present disclosure, at step 216a the one or more hardware processors 102 construct a data-driven dependency graph using the mapped positional data as a root node of a current iteration. In an embodiment of the present disclosure, at step 216b the one or more hardware processors 102 populate one or more missing values corresponding to positional data associated with a set of sensors, wherein the one or more missing values serves as a set of child nodes associated with the root node of the current iteration, and wherein the set of child nodes serves as a root node for a subsequent iteration.
[039] The above steps 216a and 216b are iteratively performed until a last child node is populated with a missing value, wherein the last child node belongs to a plurality of child nodes in the data-driven dependency graph. Below Table 13 depicts child nodes being populated (e.g., lat_pop and long_pop) in the data-driven dependency graph.
Table 13
lat_pop long_pop


37.298464 75.09474298
37.287743 75.10044087
37.289424 75.10171
37.288938 75.10066598
37.29976 75.10196098
37.27450812 357.845053
37.30069935 357.84532
0.023156 75.098148
37.24446624 282.74328
37.26534866 282.74328
-9.10875E-05 357.874701
37.29812979 357.846039
0.088573 75.078166
37.193886 75.006936
37.3 0.000873997
… …
37.289791 75.101817

[040] The one or more missing values for the set of sensors residing at the set of child nodes as shown in above Table 13 are populated based on a machine learning based prediction technique. In an embodiment of the present disclosure, missing values for rest of the sensor values, whose values are dependent on the latitude and longitude, such as fuel consumption, are obtained/populated by fitting a machine learning based prediction technique. Examples of machine learning based prediction technique, include, but are not limited to, (i) Support Vector Regression, (ii) Random Forest Regression, and (iii) Long Short-Term Memory (LSTM) based prediction technique may be used for populating the missing values corresponding to child nodes in the graph. In the above Tables 1 to 13, table cells denoting ‘…’ are indicative of in between entries with respect to first timestamp and last timestamp. Similarly, tables cells with no entries or cell with empty space depict that sensor observation is unavailable (or not captured) for the current timestamp by the device (e.g., vehicle, IoT device, car, airplane, smart device, etc.).
Results:
[041] System and method of the present disclosure conducted experiment on a dataset as applicable. The statistic of the dataset is presented in below Table 14:
Table 14
Total number of time series from different machines 15,000
Total number of Sensor used 14
Total number of sensors having at least one missing value 13
Number of layers in the D3G 4
Total number of time instances 25 million
Percentage of missing entries that were populated 17.3%

[042] The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
[043] It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g., any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g., hardware means like e.g., an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g., an ASIC and an FPGA, or at least one microprocessor and at least one memory with software processing components located therein. Thus, the means can include both hardware means and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g., using a plurality of CPUs.
[044] The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various components described herein may be implemented in other components or combinations of other components. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
[045] The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
[046] Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., be non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media.
[047] It is intended that the disclosure and examples be considered as exemplary only, with a true scope of disclosed embodiments being indicated by the following claims.